Journal of Function Spaces http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Some Topological Properties of Mon, 22 Dec 2014 00:10:16 +0000 http://www.hindawi.com/journals/jfs/2014/195262/ If is a completely regular space, first we characterize those spaces whose compact sets are metrizable. Then we use this result to provide a general condition for to ensure the metrizability of compact sets in . Finally, we characterize those spaces that have a -basis. Juan Carlos Ferrando Copyright © 2014 Juan Carlos Ferrando. All rights reserved. Lipschitz Estimates for One-Sided Cohen’s Commutators on Weighted One-Sided Triebel-Lizorkin Spaces Mon, 08 Dec 2014 12:22:45 +0000 http://www.hindawi.com/journals/jfs/2014/720875/ We introduce one-sided Cohen’s commutators of singular integral operators and fractional integral operators, respectively. Using the extrapolation of one-sided weights, we establish the boundedness of these operators from weighted Lebesgue spaces to weighted one-sided Triebel-Lizorkin spaces. Xiao Jin Zhang and Xian Ming Hou Copyright © 2014 Xiao Jin Zhang and Xian Ming Hou. All rights reserved. Weak Compactness of Almost Limited Operators Wed, 03 Dec 2014 00:10:17 +0000 http://www.hindawi.com/journals/jfs/2014/263159/ This paper is devoted to the relationship between almost limited operators and weakly compact operators. We show that if is a -Dedekind complete Banach lattice, then every almost limited operator is weakly compact if and only if is reflexive or the norm of is order continuous. Also, we show that if is a -Dedekind complete Banach lattice, then the square of every positive almost limited operator is weakly compact if and only if the norm of is order continuous. Aziz Elbour, Nabil Machrafi, and Mohammed Moussa Copyright © 2014 Aziz Elbour et al. All rights reserved. Generalized Composition Operators on Zygmund-Orlicz Type Spaces and Bloch-Orlicz Type Spaces Sun, 30 Nov 2014 07:56:56 +0000 http://www.hindawi.com/journals/jfs/2014/549370/ The boundedness and compactness of generalized composition operators on Zygmund-Orlicz type spaces and Bloch-Orlicz type spaces are established in this paper. Congli Yang, Fangwei Chen, and Pengcheng Wu Copyright © 2014 Congli Yang et al. All rights reserved. Higher Order Sobolev-Type Spaces on the Real Line Tue, 25 Nov 2014 12:26:45 +0000 http://www.hindawi.com/journals/jfs/2014/261565/ This paper gives a characterization of Sobolev functions on the real line by means of pointwise inequalities involving finite differences. This is also shown to apply to more general Orlicz-Sobolev, Lorentz-Sobolev, and Lorentz-Karamata-Sobolev spaces. Bogdan Bojarski, Juha Kinnunen, and Thomas Zürcher Copyright © 2014 Bogdan Bojarski et al. All rights reserved. Approximate Generalized Cubic -Derivations Thu, 20 Nov 2014 13:38:34 +0000 http://www.hindawi.com/journals/jfs/2014/757956/ We will show the general solution of the functional equation = and investigate the stability of cubic -derivations associated with the given functional equation on Banach -algebras. Heejeong Koh and Dongseung Kang Copyright © 2014 Heejeong Koh and Dongseung Kang. All rights reserved. Blowup of Solution for a Class of Doubly Nonlinear Parabolic Systems Tue, 18 Nov 2014 06:36:38 +0000 http://www.hindawi.com/journals/jfs/2014/924596/ An initial boundary value problem for a class of doubly parabolic equations is studied. We obtain sufficient conditions for the blowup of solutions under suitable initial data using differential inequalities. Jun Lu, Qingying Hu, and Hongwei Zhang Copyright © 2014 Jun Lu et al. All rights reserved. Existence of Nontrivial Solutions for a Critical Perturbed Quasilinear Elliptic System Mon, 17 Nov 2014 06:50:27 +0000 http://www.hindawi.com/journals/jfs/2014/758963/ We consider a perturbed quasilinear elliptic system involving the -Laplacian with critical growth terms in . Under proper conditions, we establish the existence of nontrivial solutions by using the variational methods. Huixing Zhang and Xiangzhi Zhang Copyright © 2014 Huixing Zhang and Xiangzhi Zhang. All rights reserved. On the Compactness of the Commutator of the Parabolic Marcinkiewicz Integral with Variable Kernel Wed, 12 Nov 2014 11:48:56 +0000 http://www.hindawi.com/journals/jfs/2014/693534/ The authors prove that the commutator of the parabolic Marcinkiewicz integral with variable kernel is a compact operator on if and only if . The result is substantial improvement and extension of some known results. Yanping Chen, Kai Zhu, and Yong Ding Copyright © 2014 Yanping Chen et al. All rights reserved. On Continuity of Functions between Vector Metric Spaces Wed, 12 Nov 2014 08:17:27 +0000 http://www.hindawi.com/journals/jfs/2014/753969/ We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems. Cüneyt Çevik Copyright © 2014 Cüneyt Çevik. All rights reserved. On Isometric Extension in the Space Tue, 21 Oct 2014 07:54:45 +0000 http://www.hindawi.com/journals/jfs/2014/678407/ We study the problem of isometric extension on a sphere of the space . We give an affirmative answer to Tingley’s problem in the space . Xiaohong Fu Copyright © 2014 Xiaohong Fu. All rights reserved. Marcinkiewicz Integral Operators and Commutators on Herz Spaces with Variable Exponents Wed, 15 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2014/430365/ Our aim in this paper is to give the boundedness of the Marcinkiewicz integral on Herz spaces and , where the two main indices are variable. Meanwhile, we consider the boundedness of the higher order commutator generated by and a function in BMO on these spaces. Liwei Wang Copyright © 2014 Liwei Wang. All rights reserved. Positive Solutions of a Kind of Equations Related to the Laplacian and -Laplacian Tue, 14 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2014/364010/ Positive solutions of a kind of equations related to the Laplacian and -Laplacian on a bounded domain in with are studied by using variational method. A sufficient condition of the existence of positive solutions is characterized by the eigenvalues of linear and another nonlinear eigenvalue problems. Fangfang Zhang and Zhanping Liang Copyright © 2014 Fangfang Zhang and Zhanping Liang. All rights reserved. Dual Algebras and A-Measures Mon, 13 Oct 2014 14:23:00 +0000 http://www.hindawi.com/journals/jfs/2014/364271/ Weak-star closures of Gleason parts in the spectrum of a function algebra are studied. These closures relate to the bidual algebra and turn out both closed and open subsets of a compact hyperstonean space. Moreover, weak-star closures of the corresponding bands of measures are reducing. Among the applications we have a complete solution of an abstract version of the problem, whether the set of nonnegative A-measures (called also Henkin measures) is closed with respect to the absolute continuity. When applied to the classical case of analytic functions on a domain of holomorphy , our approach avoids the use of integral formulae for analytic functions, strict pseudoconvexity, or some other regularity of . We also investigate the relation between the algebra of bounded holomorphic functions on and its abstract counterpart—the * closure of a function algebra A in the dual of the band of measures generated by one of Gleason parts of the spectrum of A. Marek Kosiek and Krzysztof Rudol Copyright © 2014 Marek Kosiek and Krzysztof Rudol. All rights reserved. A Unified Approach to Some Classes of Nonlinear Integral Equations Wed, 03 Sep 2014 10:37:32 +0000 http://www.hindawi.com/journals/jfs/2014/306231/ We are going to discuss some important classes of nonlinear integral equations such as integral equations of Volterra-Chandrasekhar type, quadratic integral equations of fractional orders, nonlinear integral equations of Volterra-Wiener-Hopf type, and nonlinear integral equations of Erdélyi-Kober type. Those integral equations play very significant role in applications to the description of numerous real world events. Our aim is to show that the mentioned integral equations can be treated from the view point of nonlinear Volterra-Stieltjes integral equations. The Riemann-Stieltjes integral appearing in those integral equations is generated by a function of two variables. The choice of a suitable generating function enables us to obtain various kinds of integral equations. Some results concerning nonlinear Volterra-Stieltjes integral equations in several variables will be also discussed. Nurgali K. Ashirbayev, Józef Banaś, and Raina Bekmoldayeva Copyright © 2014 Nurgali K. Ashirbayev et al. All rights reserved. Ulam’s Type Stability and Fixed Points Methods Wed, 03 Sep 2014 09:08:23 +0000 http://www.hindawi.com/journals/jfs/2014/465861/ Janusz Brzdęk, Liviu Cădariu, Krzysztof Ciepliński, Ajda Fošner, Zbigniew Leśniak, and Bing Xu Copyright © 2014 Janusz Brzdęk et al. All rights reserved. Locally Lipschitz Composition Operators in Space of the Functions of Bounded -Variation Mon, 01 Sep 2014 07:35:09 +0000 http://www.hindawi.com/journals/jfs/2014/606307/ We give a necessary and sufficient condition on a function under which the nonlinear composition operator , associated with the function , , acts in the space and satisfies a local Lipschitz condition. Odalis Mejía, Nelson José Merentes Díaz, and Beata Rzepka Copyright © 2014 Odalis Mejía et al. All rights reserved. A Note on Starshaped Sets in 2-Dimensional Manifolds without Conjugate Points Thu, 28 Aug 2014 11:49:42 +0000 http://www.hindawi.com/journals/jfs/2014/675735/ Let be complete, simply connected n-dimensional Riemannian manifolds without conjugate points. Assume that is starshaped where . For every point , define : y lies on some geodesic segment in S from x to a point of kerS. There is a finite collection of all maximal sets whose union is S. Further, ker in . Adem Kılıcman and Wedad Saleh Copyright © 2014 Adem Kılıcman and Wedad Saleh. All rights reserved. Existence and Uniqueness of Periodic Solutions for Second Order Differential Equations Wed, 27 Aug 2014 07:56:29 +0000 http://www.hindawi.com/journals/jfs/2014/246258/ We study some second order ordinary differential equations. We establish the existence and uniqueness in some appropriate function space. By using Schauder’s fixed-point theorem, new results on the existence and uniqueness of periodic solutions are obtained. Yuanhong Wei Copyright © 2014 Yuanhong Wei. All rights reserved. Spectral Distribution of Transport Operator Arising in Growing Cell Populations Mon, 25 Aug 2014 10:46:44 +0000 http://www.hindawi.com/journals/jfs/2014/748792/ Transport equation with partly smooth boundary conditions arising in growing cell populations is studied in space. It is to prove that the transport operator generates a semigroup and the ninth-order remainder term of the Dyson-Phillips expansion of the semigroup is compact, and the spectrum of transport operator consists of only finite isolated eigenvalues with finite algebraic multiplicities in a trip . The main methods rely on theory of linear operators, comparison operators, and resolvent operators approach. Hongxing Wu, Shenghua Wang, and Dengbin Yuan Copyright © 2014 Hongxing Wu et al. All rights reserved. The Boundedness of Marcinkiewicz Integrals Associated with Schrödinger Operator on Morrey Spaces Wed, 20 Aug 2014 11:10:55 +0000 http://www.hindawi.com/journals/jfs/2014/901267/ Let be a Schrödinger operator, where belongs to some reverse Hölder class. The authors establish the boundedness of Marcinkiewicz integrals associated with Schrödinger operators and their commutators on Morrey spaces. Dongxiang Chen and Fangting Jin Copyright © 2014 Dongxiang Chen and Fangting Jin. All rights reserved. Spaces on the Unit Circle Wed, 20 Aug 2014 06:25:02 +0000 http://www.hindawi.com/journals/jfs/2014/234790/ We introduce a new space of Lebesgue measurable functions on the unit circle connecting closely with the Sobolev space. We obtain a necessary and sufficient condition on such that , as well as a general criterion on weight functions and , , such that . We also prove that a measurable function belongs to if and only if it is Möbius bounded in the Sobolev space . Finally, we obtain a dyadic characterization of functions in spaces in terms of dyadic arcs on the unit circle. Jizhen Zhou Copyright © 2014 Jizhen Zhou. All rights reserved. -Contractive Mappings on Generalized Quasimetric Spaces Mon, 18 Aug 2014 07:41:53 +0000 http://www.hindawi.com/journals/jfs/2014/914398/ We consider the existence of a fixed point of -contractive mappings in the context of generalized quasimetric spaces without Hausdorff assumption. The obtained results extend several results on the topic in the literature. Erdal Karapınar and Hosein Lakzian Copyright © 2014 Erdal Karapınar and Hosein Lakzian. All rights reserved. Anisotropic Two-Microlocal Spaces and Regularity Sun, 17 Aug 2014 12:24:05 +0000 http://www.hindawi.com/journals/jfs/2014/505796/ We define --anisotropic two-microlocal spaces by decay conditions on anisotropic wavelet coefficients on any --anisotropic wavelet basis of . We prove that these spaces allow the characterizing of pointwise anisotropic Hölder regularity. We also prove an anisotropic wavelet criterion for anisotropic uniform regularity. We finally prove that both this criterion and anisotropic --two-microlocal spaces are independent of the chosen anisotropic --orthonormal wavelet basis. Mourad Ben Slimane Copyright © 2014 Mourad Ben Slimane. All rights reserved. Stability for the Mixed Type of Quartic and Quadratic Functional Equations Sun, 17 Aug 2014 11:31:53 +0000 http://www.hindawi.com/journals/jfs/2014/853743/ We establish the general solutions of the following mixed type of quartic and quadratic functional equation: . Moreover we prove the Hyers-Ulam-Rassias stability of this equation under the approximately quartic and the approximately quadratic conditions. Young-Su Lee, Soomin Kim, and Chaewon Kim Copyright © 2014 Young-Su Lee et al. All rights reserved. The Relationship between Two Involutive Semigroups and Is Defined by a Left Multiplier T Sun, 17 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2014/851237/ Let be a semigroup with a left multiplier T on . There exists a new semigroup , which depends on and T, which has the same underlying space as . We study the question of involutions on and a Banach algebra . We find a condition of T under which and the second dual admit an involution. We will show that is -algebra if and only if is an isometry, under mild conditions. Also, is -algebra if and only if so is , under other minor conditions. S. M. Mohammadi and J. Laali Copyright © 2014 S. M. Mohammadi and J. Laali. All rights reserved. Fixed Point Theory and the Ulam Stability Wed, 13 Aug 2014 09:14:40 +0000 http://www.hindawi.com/journals/jfs/2014/829419/ The fixed point method has been applied for the first time, in proving the stability results for functional equations, by Baker (1991); he used a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single variable. However, most authors follow the approaches involving a theorem of Diaz and Margolis. The main aim of this survey is to present applications of different fixed point theorems to the theory of stability of functional equations, motivated by a problem raised by Ulam in 1940. Janusz Brzdęk, Liviu Cădariu, and Krzysztof Ciepliński Copyright © 2014 Janusz Brzdęk et al. All rights reserved. Riesz Basicity for General Systems of Functions Tue, 12 Aug 2014 09:14:46 +0000 http://www.hindawi.com/journals/jfs/2014/860279/ In this paper we find the general conditions for a complete biorthogonal conjugate system to form a Riesz basis. We show that if a complete biorthogonal conjugate system is uniformly bounded and its coefficient space is solid, then the system forms a Riesz basis. We also construct affine Riesz bases as an application to the main result. A. M. Sarsenbi and P. A. Terekhin Copyright © 2014 A. M. Sarsenbi and P. A. Terekhin. All rights reserved. Existence of Positive Solutions for Some Superlinear Fourth-Order Boundary Value Problems Mon, 11 Aug 2014 06:11:18 +0000 http://www.hindawi.com/journals/jfs/2014/384958/ We are concerned with the following superlinear fourth-order equation , where are nonnegative constants such that and is a nonnegative continuous function that is required to satisfy some appropriate conditions related to a class satisfying suitable integrability condition. Our purpose is to prove the existence, uniqueness, and global behavior of a classical positive solution to the above problem by using a method based on estimates on the Green function and perturbation arguments. Imed Bachar and Habib Mâagli Copyright © 2014 Imed Bachar and Habib Mâagli. All rights reserved. A Mathematical Analysis of Fractional Fragmentation Dynamics with Growth Thu, 07 Aug 2014 10:40:34 +0000 http://www.hindawi.com/journals/jfs/2014/201520/ We make use of the theory of strongly continuous solution operators for fractional models together with the subordination principle for fractional evolution equations (Bazhlekova (2000) and Prüss (1993)) to analyze and show existence results for a fractional fragmentation model with growth characterized by its growth rate . Indeed, strange phenomena like the phenomenon of shattering (McGrady and Ziff (1987)) and the sudden appearance of infinite number of particles in some systems with initial finite particles number could not be fully explained by classical models of fragmentation or aggregation. Then, there is an increasing volition to try new approaches and extend classical models to fractional ones. In the growth model, one of the major challenges in the analysis occurs when is integrable at , the minimum size of a cell. We restrict our analysis to the case of integrability of at . This case needs more considerations on the boundary condition, which, in this paper, is the McKendrick-von Foerster renewal condition. In the process, some properties of Mittag-Leffler relaxation function Berberan-Santos (2005) are exploited to finally prove that there is a positive solution operator to the full model. Emile Franc Doungmo Goufo Copyright © 2014 Emile Franc Doungmo Goufo. All rights reserved.